This invention relates generally to computed tomography (CT) and more particularly to matched view weighting methods for computed tomography scanners using multiple tilted reconstruction planes.
A single tilted-plane-based reconstruction (sTPR) algorithm has been proposed to combat cone beam and helical artifacts in helical multi-detector-row CT. Each tilted reconstruction plane (RP) in sTPR uses two freedoms of rotation. A virtual x-ray source trajectory (VT) is defined as the intersection of a RP with the cylinder containing an actual helical x-ray source trajectory (AT) to reconstruct an image on each tilted RP. The error between VT and AT (namely trajectory error) is globally minimized and symmetric if the central intersection point between a RP and an AT is taken as the origin. However, noise characteristics of sTPR may be compromised because only short scan (180xc2x0+fan angle) projection data are used to reconstruct an image on a tilted RP. To improve the noise characteristics of sTPR, a multiple-tilted-plane-based reconstruction (mTPR) algorithm has been proposed, in which each tilted RP uses three freedoms of rotation. As a result, the trajectory error in mTPR is no longer globally minimized and symmetric.
In one aspect, a method for Computed Tomography scanners using multiple tilted reconstruction planes is provided. The method includes view weighting data in accordance with       χ    ⁡          (              β        ,        γ            )        =      {                                        w            b                                                0            ≤            β            ≤                                          2                ⁢                                  xe2x80x83                                ⁢                                  γ                  m                                            -                              2                ⁢                                  xe2x80x83                                ⁢                γ                                                                          1                                                                                      2                  ⁢                                      xe2x80x83                                    ⁢                                      γ                    m                                                  -                                  2                  ⁢                                      xe2x80x83                                    ⁢                  γ                                             less than               β              ≤                              π                -                                  2                  ⁢                                      xe2x80x83                                    ⁢                  γ                  ⁢                                      xe2x80x83                                    ⁢                                      ω                    ⁡                                          (                                              β                        ,                        γ                                            )                                                                                            =                                                            xe2x80x83                                                              3              ⁢                              xe2x80x83                            ⁢                                                χ                  2                                ⁡                                  (                                      β                    ,                    γ                                    )                                                      -                          2              ⁢                              xe2x80x83                            ⁢                                                χ                  3                                ⁡                                  (                                      β                    ,                    γ                                    )                                            ⁢                              xe2x80x83                            ⁢              where              ⁢                              xe2x80x83                            ⁢              β                                                                        w            t                                                              π              -                              2                ⁢                                  xe2x80x83                                ⁢                γ                                       less than             β            ≤                          π              +                              2                ⁢                                  xe2x80x83                                ⁢                                  γ                  m                                                                        
is a central view angle, xcex3 is a fan angle, xcex3m is a maximum half fan angle of an x-ray beam, and wb and wt are each weights no greater than 1.
In another aspect, a Computed Tomography (CT) system includes an x-ray source, a detector positioned to receive x-rays emitted from the source, and a computer operationally coupled to the source and the detector. The computer is configured to receive data from a scan of an object, and weight the received data in accordance with       χ    ⁡          (              β        ,        γ            )        =      {                                        w            b                                                0            ≤            β            ≤                                          2                ⁢                                  xe2x80x83                                ⁢                                  γ                  m                                            -                              2                ⁢                                  xe2x80x83                                ⁢                γ                                                                          1                                                                                      2                  ⁢                                      xe2x80x83                                    ⁢                                      γ                    m                                                  -                                  2                  ⁢                                      xe2x80x83                                    ⁢                  γ                                             less than               β              ≤                              π                -                                  2                  ⁢                                      xe2x80x83                                    ⁢                  γ                  ⁢                                      xe2x80x83                                    ⁢                                      ω                    ⁡                                          (                                              β                        ,                        γ                                            )                                                                                            =                                                            xe2x80x83                                                              3              ⁢                              xe2x80x83                            ⁢                                                χ                  2                                ⁡                                  (                                      β                    ,                    γ                                    )                                                      -                          2              ⁢                              xe2x80x83                            ⁢                                                χ                  3                                ⁡                                  (                                      β                    ,                    γ                                    )                                            ⁢                              xe2x80x83                            ⁢              where              ⁢                              xe2x80x83                            ⁢              β                                                                        w            t                                                              π              -                              2                ⁢                                  xe2x80x83                                ⁢                γ                                       less than             β            ≤                          π              +                              2                ⁢                                  xe2x80x83                                ⁢                                  γ                  m                                                                        
is a central view angle, xcex3 is a fan angle, xcex3m is a maximum half fan angle of an x-ray beam, and wb and wt are each weights no greater than 1.
In another aspect, a method of obtaining and using weights is provided. The method includes setting       w    b    =                              e          t                                      e            t                    +                      e            b                              ⁢              xe2x80x83            ⁢      and      ⁢              xe2x80x83            ⁢              w        t              =                  e        b                              e          t                +                  e          b                    
with             e      b        =                  ∫        0                              π            2                    +                      γ            m                              ⁢                        "LeftBracketingBar"                                    A              ⁢                              xe2x80x83                            ⁢                              T                ⁡                                  (                  β                  )                                                      -                          V              ⁢                              xe2x80x83                            ⁢                              T                ⁡                                  (                  β                  )                                                              "RightBracketingBar"                ⁢                  ⅆ          β                ⁢                  xe2x80x83                ⁢        and                        xe2x80x83        ⁢                  e        t            =                        ∫                                    π              2                        +                          γ              m                                            π            +                          2              ⁢                              xe2x80x83                            ⁢                              γ                m                                                    ⁢                              "LeftBracketingBar"                                          A                ⁢                                  xe2x80x83                                ⁢                                  T                  ⁡                                      (                    β                    )                                                              -                              V                ⁢                                  xe2x80x83                                ⁢                                  T                  ⁡                                      (                    β                    )                                                                        "RightBracketingBar"                    ⁢                      ⅆ            β                              
wherein AT(xcex2) is an actual helical x-ray source trajectory (AT) of xcex2 and VT(xcex2) is a virtual x-ray source trajectory (VT) of xcex2, and weighting image data with wb and wt prior to filtering and backprojecting the image data to reconstruct an image.
In still another aspect, a computer readable medium encoded with a program configured to instruct a computer is provided. The program is configured to instruct the computer to receive data from a scan of an object, and weight the received data in accordance with       χ    ⁡          (              β        ,        γ            )        =      {                                        w            b                                                0            ≤            β            ≤                                          2                ⁢                                  xe2x80x83                                ⁢                                  γ                  m                                            -                              2                ⁢                                  xe2x80x83                                ⁢                γ                                                                          1                                                                                      2                  ⁢                                      xe2x80x83                                    ⁢                                      γ                    m                                                  -                                  2                  ⁢                                      xe2x80x83                                    ⁢                  γ                                             less than               β              ≤                              π                -                                  2                  ⁢                                      xe2x80x83                                    ⁢                  γ                  ⁢                                      xe2x80x83                                    ⁢                                      ω                    ⁡                                          (                                              β                        ,                        γ                                            )                                                                                            =                                                            xe2x80x83                                                              3              ⁢                              xe2x80x83                            ⁢                                                χ                  2                                ⁡                                  (                                      β                    ,                    γ                                    )                                                      -                          2              ⁢                              xe2x80x83                            ⁢                                                χ                  3                                ⁡                                  (                                      β                    ,                    γ                                    )                                            ⁢                              xe2x80x83                            ⁢              where              ⁢                              xe2x80x83                            ⁢              β                                                                        w            t                                                              π              -                              2                ⁢                                  xe2x80x83                                ⁢                γ                                       less than             β            ≤                          π              +                              2                ⁢                                  xe2x80x83                                ⁢                                  γ                  m                                                                        
is a central view angle, xcex3 is a fan angle, xcex3m is a maximum half fan angle of an x-ray beam, and wb and wt are each weights no greater than 1.